If `tan^3A+tan^3B+tan^3C=3tanA* tanB*tanC ,` then prove that triangle ABC is an equilateral triangle.

If in a Delta ABC, cosA+ cosB + cosc =3/2. Prove that DeltaABC is an equilateral triangle.

In triangleABC , if sqrt(3)sin C=2 sec A-tan A , then prove that triangle is right angled.

In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tanA/2tanA/2+tanB/2| then the triangle must be a. equilateral b. isosceles c. obtuse angled d. none of these

If tan(A+B)=3 tan A , prove that (a) sin(2A+B)=2sin B

Find the length of the side and perimeter of an equilateral triangle whose height is sqrt 3 cm . (i) Delta ABC is an " equilateral triangle" . (ii) "seg" AM bot side BC, B - M - C (iii) AM = sqrt 3 cm

If in a Delta ABC ,tanA+tanB+tanC=6, then cotA cotB cotC=

In triangle A B C ,tan(A-B)+tan(B-C)+"tan"(C-A=0. Prove that the triangle isisoceles.

If tan A=1//2, tan B=1//3 , then prove that cos 2A=sin2B .

In triangle ABC, if |[1,1,1], [cot (A/2), cot(B/2), cot(C/2)], [tan(B/2)+tan(C/2), tan(C/2)+ tan(A/2), tan(A/2)+ tan(B/2)]| then the triangle must be (A) Equilateral (B) Isoceless (C) Right Angle (D) none of these